Image and video signal processing is widely used in a number of applications today. Often a need arises for an image or video of a particular resolution and only an image or video of a lower resolution is available. In such a case, there are a number of methods that are used to use the lower resolution version to create an image of higher resolution. These existing methods include applying linear or simple non-linear interpolation filters to the lower resolution image or video.
Examples of the use of linear or non-linear interpolation filters include a bilinear interpolation filter such as described in Gonzalez & Woods, “Digital Image Processing”, Pearson Education, 2nd Edition; a linear interpolation filter described in ITU-T Recommendation H.264 & ISO/IEC 14496-10 (MPEG-4) AVC, “Advanced Video Coding for Generic Audiovisual Services”, version 3: 2005; and a non-separable interpolation filter described in Vatis & Ostermann, “Locally Adaptive Non-Separable Interpolation Filter for H.264/AVC”, IEEE ICIP, October 2006. However, each of these three techniques is applicable on image/video frames that have smoothly varying pixel values. This is because they are derived using smooth image models and the filters are typically restricted to lowpass filters. Thus, they are not applicable on many types of regions, such as on slant edges, textures etc. Furthermore, at least with respect to ITU-T Recommendation H.264 and Vatis & Ostermann, the techniques are applicable only in a video compression application where previous frame(s) shifted by a fraction of pixel is/are used to predict the current frame.
Also, very simple transform-based methods exist for increasing the resolution of an image/video, but require a large number of iterations. One such example is described in Guleryuz, “Predicting Wavelet Coefficients Over Edges Using Estimates Based on Nonlinear Approximants”, Proc. Data Compression Conference, April 2004. However, this technique is limited to block transforms with various simplifications that are not applicable on slant edges and textures and involves many iterations of a basic method to get good quality and the complexity is prohibitively expensive.